Metamath Proof Explorer

Definition df-hlo

Description: Define the class of all complex Hilbert spaces. A Hilbert space is a Banach space which is also an inner product space. (Contributed by Steve Rodriguez, 28-Apr-2007) (New usage is discouraged.)

Ref Expression
Assertion df-hlo CHil OLD = CBan CPreHil OLD

Detailed syntax breakdown

Step Hyp Ref Expression
0 chlo class CHil OLD
1 ccbn class CBan
2 ccphlo class CPreHil OLD
3 1 2 cin class CBan CPreHil OLD
4 0 3 wceq wff CHil OLD = CBan CPreHil OLD